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A151310
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, -1), (1, 1)}
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1
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1, 2, 9, 37, 181, 869, 4430, 22640, 118808, 627275, 3358307, 18087833, 98248087, 536372711, 2945032779, 16237200915, 89896571332, 499383074373, 2783038880080, 15552412965005, 87134774936870, 489297438647055, 2753406974342080, 15523739339340106, 87677875795392958, 496006562740402954
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OFFSET
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0,2
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LINKS
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M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MAPLE
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steps:= [[-1, -1], [-1, 1], [-1, 0], [0, 1], [1, -1], [1, 1]]:
f:= proc(n, p) option remember; local t;
if n <= min(p) then return 6^n fi;
add(procname(n-1, t), t=remove(has, map(`+`, steps, p), -1));
end proc:
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MATHEMATICA
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aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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